Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
224 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. Q16×#10596831 | C2 | semidirect |
| 3. #22608003 | C2 | semidirect |
| 4. #22607895 | C2 | semidirect |
| 6. #22607850 | C2 | semidirect |
| 55. Q16×C73 | M16 | semidirect |
| 113. C73 | #12075 | semidirect |
| 154. Q16 | #11924012 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22608816 | 2 |
| Q16×#10596831 | 2 |
| #22608003 | 2 |
| #22607895 | 2 |
| #22607892 | 2 |
| #22607850 | 2 |
| C4×SD32×C73 | 2 |
| #12075 | 73 |